Unlike most of the contradictions which sceptics claim to have found in the Bible, this one is a little more tricky to answer, since it relies upon delving somewhat into the Hebrew itself to explain artifices of that language which are not readily apparent when translated into English. Let us begin by first looking at the two passages and noting some things,
"And the Syrians fled before Israel; and David slew the men of seven hundred chariots of the Syrians, and forty thousand horsemen, and smote Shobach the captain of their host, who died there." (II Samuel 10:18)
"But the Syrians fled before Israel; and David slew of the Syrians seven thousand men which fought in chariots, and forty thousand footmen, and killed Shophach the captain of the host." (II Chronicles 19:18)
Notice that the phrases "the men of" and "men which fought in" are italicised. This means that they do not appear in the original text, but were supplied by the King James translators to give a clearer understanding of the sense of the passage. As it turns out, these supplied words are quite correct in explaining, textually and contextually, what is going on in these passages.
Obviously, one does not slay chariots. As non-living objects, chariots are (of course) incapable of dying. Yet, the original Hebrew (remember, without the supplied words) is essentially saying that David killed these chariots, which is what the literal reading says. What must be understood, however, is that this sort of construction is an artifice of the Hebrew language which is used to refer to something associated with the object in question. This ought to be clearly shown when we examine another passage where this same sort of artifice is used, except it more explicitly shows what is going on. II Chronicles 18:4 says concerning another of David's victories over the Syrians,
"And David took from him a thousand chariots, and seven thousand horsemen, and twenty thousand footmen: David also houghed all the chariot horses, but reserved of them an hundred chariots."
Notice that here, the word "horses" is also supplied - it does not appear in the original text. The word "horses" is implied, though, again because of the fact that you do not "hough" (or hamstring) chariots. This is something done to horses so that they cannot run, and thus be useful in warfare. The context clearly demonstrates that it is the horses being houghed, not the chariots. Also, the construction of the Hebrew itself shows the same. The phrase used to denote the chariots is "eth-kal-rekev" (bk#r#h*-lK*-ta#). "Rekev" is the Hebrew word for "chariot". "Eth" is a particle in Hebrew which denotes that the object following the maqqeph (the dash) is the object of the verb, in other words it is telling us explicitly that the chariots are the object of the verb "hough". "Kal" is another particle which denotes the completeness of the action, basically it means "all", and is denoting that all the "chariots" have been houghed. Yet, we see that right after this statement, David is said to have reserved a hundred chariots out of what he took as booty. Thus, the text is saying that ALL the chariots were houghed, yet in the next clause, David reserves a hundred chariots for use. Obviously, what is being houghed is not the chariots themselves (which is nonsensical anywise), but rather the horses associated with the chariots. This is what the context of the passage demands, and is not necessarily illogical when we note that chariots and horses together represent a fighting unit, so it is not surprising that the ancients considered horses almost as a part of the chariots, even though we may be more discriminating in our terminology.
Back to the issue at hand, we then see that the two statements, whereby David destroyes 700 chariots in one, and 7,000 chariots in the other, need not be understood as a contradiction for the simple reason that, as with 18:4, the context demands that something associated with the chariots be the object of discussion. As noted before, one obviously does not kill a chariot. But, in ancient warfare one COULD kill the men associated with the chariot. Again, a chariot was useless without men to operate it, fight from it, and maintain it on the battlefield. Chariots were the "tanks" of ANE warfare, and like tanks, needed men both to operate and to maintain them. The supplied phrases in the KJV with regard to these two passages are entirely logical then, considering what we've seen. In II Samuel 10:18, where 700 chariots are slain, it makes perfect contextual sense to see that it is the "men of" 700 chariots who are being slain. Likewise, the 7,000 in I Chronicles 19:18 is logically and contextually understood to be "men who fought in" these chariots. The numbers, 700 and 7,000, are likewise wholly reconcilable when viewed this way. It is quite likely that around 7,000 men would be needed in an ancient army to field 700 chariots, considering that a chariot crew consisted not only of the driver and the archer/spear-thrower, but also men to fix any damaged or broken wheels and axles, men to maintain supplies for the team, men to take care of the horses, etc.
Now let's turn to the issue of the apparent contradiction between "horsemen" in II Samuel 10:18 and "footmen" in I Chronicles 19:18. This one is quite easy to answer, when we remember that the book of II Samuel was written sometime around the middle part of the 10th century BC, roughly 950 BC. I Chronicles, on the other hand, is much later, being written in the post-exilic period around 450-425 BC. This is important information because what we see in the difference in readings between the two passages reflects the changes which had occurred in ANE warfare between the times of the two writings (and which actually helps to affirm the authenticity and dating of both passages, rather than detracting from them!)
We need to understand that when the Bible uses the term "horsemen" in I Samuel 10:18, this term is not necessarily to be understood in the same sense that we think of it, as armed, mounted cavalry. Indeed, among Semitic groups of the ANE, cavalry as it is usually thought of did not find significant military use until toward the middle part of the first millennium BC. It was a relatively late development in warfare for the nations of the area, not being introduced to them until well into the Iron Age, a good century or more after the time of David and Solomon1. Any "cavalry" to speak of in David's day might well have used mules, rather than horses. Horses, to the extent that they found military application, were used to drive chariots, and to carry men into battle, men who would then dismount and fight on foot. The horses were used as quick and mobile transportation, but not as battle platforms, at least in the time period when II Samuel was written. Thus, when the Bible at this point refers to "horsemen" in this army that David defeated, it is quite likely referring to men who were carried to the battle on horseback, and who then dismounted and fought on foot.
By the time that I Chronicles was written (in the post-exilic, Persian period), this situation had changed drastically. Chariots had gone the way of the zepellin, and were replaced by the rudiments of true cavalry. As Barton says,
"By the middle of the first millennium chariots were relegated to roles of transport. Mobile assault units were then fielded as cavalry, although their full potential would not be exploited for centuries, until the invention of the stirrup allowed the rider to steer the horse with his feet and freed his hands for use of a weapon."2
To a person in that day, a "horseman" would conjure up images of a man who fought from horseback, rather than dismounting and fighting on foot. Thus, the fact that I Chronicles changes the terminology and uses "footmen" instead of "horsemen" reflects an accurate depiction of the changed situation. Whereas in 950 BC these men would be referred to as "horsemen" for their transportation scheme, this term took on a different meaning later, and they were referred to as "footmen" since they fought on foot.
As such, there is no real contradiction between these two passages on any count. The first half of the "contradiction" requires some investigation into the Hebrew, but the context clearly shows that both the statements themselves, as well as the translation and supplied words, are accurate and correct. The second half is answered by simply looking at the basic changes made in warfare in the ANE between the two time periods during which the two books were written.
(1) - see Y. Yadin, The Art of Warfare in Biblical Lands, Vol. II, p. 287
(2) - The Biblical World, ed. J. Barton, Vol. II, p. 35
(1) - see Y. Yadin, The Art of Warfare in Biblical Lands, Vol. II, p. 287